Problem: Simplify the following expression: $ q = 1 - \dfrac{-7z + 10}{-8z} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-8z}{-8z}$ $ \dfrac{1}{1} \times \dfrac{-8z}{-8z} = \dfrac{-8z}{-8z} $ Therefore $ q = \dfrac{-8z}{-8z} - \dfrac{-7z + 10}{-8z} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-8z - (-7z + 10) }{-8z} $ Distribute the negative sign: $q = \dfrac{-8z + 7z - 10}{-8z}$ $q = \dfrac{-z - 10}{-8z}$ Simplify the expression by dividing the numerator and denominator by -1: $q = \dfrac{z + 10}{8z}$